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If the circle x^2+y^2=a^2 intersects the...

If the circle `x^2+y^2=a^2` intersects the hyperbola `x y=C^2` at four points `P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3),` and `S(x_4, y_4),` then proove `x_1+x_2+x_3+x_4=0`, `y_1+y_2+y_3+y_4=0`, `x_1x_2x_3x_4=C^4`, `y_1``y_2``y_3``y_4`=`C^4`

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